The two "before" and "after" photographs (Figures 1 and 2) illustrate the effect of a "100-year avalanche" in the Deadman Gulch path, Colorado Front Range. Figure 1, taken in 1976, shows the results of repeated small avalanches over a period of decades. Most slides had been channelized down the gully on the left side of the fan, whereas an occasional larger slide had overtopped the gully and run out on the steep alluvial fan. Figure 2 was taken in May, 1984 after a major drysnow/powder avalanche. This event far exceeded previous path boundaries and destroyed many acres of lodgepole pine forest that had colonized the runout zone since the last major avalanche occurred at least 100 years earlier.

This Deadman Gulch sequence provides valuable beforeand-after documentation of the "design avalanche," in this case, an avalanche with a return period of approximately 100 years. Similar to the traditions already established in hydrology and floodplain planning, extent of the design avalanche is often information required in planning mountain areas. This is particularly true when fixed facilities of "high risk" (buildings, parking areas, public facilities, etc.) are planned near potential runout zones.

Research on the characteristics and effects of the design avalanche has been an important topic for the past three decades in parts of Europe. Many European areas have had dense mountain populations for decades or centuries with numerous activities and structures exposed to avalanches. However, similar research efforts have not taken place in the United States, which has only recently seen significant expansion of year-round population into avalanche terrain. Avalanches, in contrast to floods, for example, affect only a very small part of the U.S. population. Therefore avalanches, unlike floods, are not considered to be "national problems" and very little tradition exists within the United States with respect to planning for unusual avalanches. Geologists and engineers cannot receive training in the methods available for "designavalanche" delineation and planning. The U.S. government no longer sponsors research on avalanche-engineering problems. Consequently, the community of avalanche professionals in the U.S. must rely primarily on research conducted in other countries and on analogies with other similar geophysical processes in order to define the design event.

This- article ..discusses. the problems and methods used to estimate design avalanche size and discusses in general terms some of the approaches used in engineering analysis. Methods available include (a) direct observations and avalanche history, (b) statistical runout-distance models, and (c) physical (mathematical) models of avalanche motion. Each method has important advantages and limitations, as briefly discussed.

DIRECT OBSERVATIONSOR HISTORY

When a very long and continuous history of avalanche events in a particular path is available, the historical method is certainly the most reliable in assessing avalanche extent. However, the detailed historical record should be 2 or 3 times longer than the return period one wishes to predict. Unfortunately, a long and continuous history rarely exists in paths where analysis is required. Figure 3 shows the probability that a 100year avalanche will occur within various observation periods.

Obviously, there is no "guarantee" that a"100-year" avalanche will occur even during a long observation period where all events are recorded. For example, there exists only a 63% chance that the 100-year avalanche will occur (more than a 1 in 3 chance it will not occur) even if the period is 100 years long. In fact, to be 95% certain that a 100-year avalanche will not reach a certain spot, that spot must have been avalanche-free for 300 years! This is true because the 100-year avalanche has a constant 1% annual probability each year. Because this probability is assumed constant every year the 100year avalanche may occur on successive years or not for many centuries.

In the United States, we must usually rely on a very short period of avalanche observation (typically 10-30 years). Reference to Figure 3 indicates a very small probability (approximately 10-25%) that the 100-year avalanche would occur during such a short time. Regardless of how good the avalanche records are, there is no logical way to use a short record to estimate the size of the rare avalanche event unless there is clear evidence through history, vegetation damage, or the recent geologic record that the design avalanche just happened recently. Furthermore, the Deadman Gulch example shows how the design event can be many times larger and more destructive than slides usually observed.

Although direct observations of past avalanches in a given path generally provide limited useful data about the extreme event, the historical record can sometimes be extended considerably by studying vegetation patterns, species distributions, and using tree-ring dating techniques. These "silent witnesses" of past events should always be consulted when available. Unfortunately, however, mature forests and other vegetation clues are often not available or have been removed from runout zones by human activity. This fact means that indirect techniques (statistical and physical models) should be used to objectively predict avalanche runout distance and extent.

STUDY OF EXTREME AVALANCHESSTATISTICAL MODELS

Avalanche-engineering specialists have for decades attempted to devise methods through which extreme avalanches could be predicted in areas where the historical record is short or discontinuous. In older to be acceptable, such a method had to objective and based on accepted scientific procedures.

In my opinion, the most promising methods for determining avalanche runout use statistical models. The data sets used in statistical models consist entirely of rare events with approximately 100-year return periods obtained in the mountain range of interest. Although the 100year event is by definition a rare event in any particular path, many such events occur throughout an entire mountain range. My personal observations in many mountain areas indicate that 100-year avalanches occur somewhere in each mountain range every few years because unique snowpack and snowloading conditions develop at least in some isolated areas in all but very dry winters. Nature is always in the process of running a great experiment on all natural phenomena, including avalanches. The statistical method simply uses the existing data already provided by nature's big experiment.

Research on statistical runout-distance models conducted during the past 10 to 15 years has observed examples of extreme avalanche runout distances, and has related these measured distances to other features of the avalanche path that could also be measured. Only rare events were included in data collection. In order to be included in the data set, avalanches had to have reached populated areas previously untouched by slides for a century or more or had to destroy portions of forests at least a century old. Avalanches of all sizes, shapes and orientations were used in the data sets collected in Norway and No rh America.

The statistical models have been applied most successfully within the Western Fiords of Norway by the Norwegian Geotechnical Institute (the "NGI Method"), where a long history of many avalanche paths is available in populated areas. This method is diagrammed in Figure 4 where an avalanche profile is shown and 3 observations are recorded: (1) The alpha angle (a) is measured from the crown location to a tip of the runout; (2) The point where the local profile slope becomes 10 degrees is identified; and (3) The beta angle ) is measured from the 10 degrees point to the crown location.

Statistical analysis of more than 200 extreme avalanche events in western Norway has shown that the alpha angle can be predicted simply by measuring the beta angle and applying a simple statistical relationship which has been derived from the data:

a=X1 b+X2

where values for Xl and X2 result from analysis of the data.

Although this method has proven very reliable, it is, or course, not perfect even in Norway. Some uncertainty exists in the prediction of the alpha angle; however, the level of this uncertainty can be specified in standard statistical terms. One may say, for example, that the predicted runout position will not be exceeded more than 5 % or 10% of the time, and base that conclusion on the analysis of a real data set that consists entirely of "100-year" avalanches in the mountain area. This is obviously more objective than simply guessing where an avalanche might stop; the predicted runout distance can be related to avalanche performance in a given region. Furthermore, no assumptions need to be made about snow type, avalanche form, or friction. In fact, the avalanches comprising the data set probably were caused by a variety of snow conditions.

Recent work I have conducted on large data sets in Colorado, the Eastern Sierra Nevada, and Coastal Alaska has shown that the calculated stopping positions based on Norway data tend to under-predict avalanche stopping positions in these North American areas. This means that the constant teens Xt and X2 require adjustment in other areas, or perhaps an additional term should be added to Equation (1). Apparently, unique relationships must be derived for each mountain region, as might logically be expected because the terrain and snow conditions that control avalanche stopping positions may differ between these areas even during the extreme events of interest in planning and engineering. However, strong positive correlations between alpha and beta do exist in all mountain areas studied and my preliminary study shows that unique statistical relationships can be derived for each of the areas.

Although the statistical methods do provide a rational and objective basis for predicting designavalanche stopping position, they do not predict avalanche lateral extent or velocity. Lateral extent must be determined subjectively, based on knowledge of avalanche behavior in the area or the locations of topographic barriers. Velocity, however, should be calculated rather than estimated because it is very important in engineered design of avalanche defense structures. For such calculations, we must turn to physical models, as discussed next.

PHYSICAL (MATHEMATICAL) AVALANCHE MODELS

Physical models have been used to predict avalanche velocity and runout distance since the 1950's, particularly in Central Europe and to a lesser extent in North America and Japan. In some areas they are used in development of avalanchezoning plans and in design of structural defenses. Because estimates of potential velocities and forces are critical in engineered design of structural defenses they must be determined by some objective criteria as is traditional in all geophysical analyses.

Early models treated avalanche motion as a modified fluid or as a center-of-mass moving along the path profile. More recent models are less restrictive, allowing predicted avalanche stopping positions to be specified in 2 or 3 dimensions, thereby adding height and width to the length dimension of earlier models. These physical or mathematical models tend to be much more complicated than the simple statistical models discussed in the previous section because they must carefully represent avalanche terrain and internal material properties and consider the interaction of all these factors in calculations of velocity and runout distance.

All physical models work essentially as diagrammed in Figure 5.

a. The physical model is written so that velocities and runout distances are computed given information about path terrain and avalanche material properties;

b. The terrain (steepness, roughness, curvature, length, channelization, etc.) are measured and used by the physical model;

c. Avalanche material properties (turbulence, viscosity, particle sizes, densities, etc.) are assumed, based on the experience of the user, and are also stored in the model;

d. The model is run, uses the values of terrain and material properties, and computes velocity, stopping position, and possibly vertical and lateral extent.

A major limitation of any physical model, regardless of its complexity, is difficulty in accurately representing the terrain and material properties in the model. The path slope, roughness, curvature, and degree of channelization are often available through topographic-map analysis and ground surveys, but the model may not be capable analyzing some of the important terrain variables. The material properties are even more difficult to specify accurately because few measurements of avalanche friction, fluid properties, densities, and particles sizes exist. Those who have been caught in major slides may have some opinions about the internal structure of avalanches, but it is understandable that no quantitative data have been taken in these circumstances! Most observers are familiar with the complexity of real avalanche terrain and have seen how cliffs, gullies, trees, open slopes, etc., tend to disrupt, retard, dissipate, and condense avalanche flow, thereby strongly affecting velocity and runout. We also have many observations of avalanches changing form considerably during descent as they encounter different types of terrain and snow type. Because avalanches often do change form over the path, this suggests the material properties, friction, and the representation of these factors in any model may also change as an avalanche descends. A physical model that may be appropriate in the upper part of the path may be inappropriate in the lower path. As diagrammed in Figure 5, values of the assumed friction terms alone can produce wide variation in the predicted stopping position of an avalanche. One set of assumptions may stop the avalanche at point "A," while other different assumptions may predict a stop at "B" or "C" This means that results derived from the use of physical models may be somewhat subjective because the stopping position (and velocities) depend upon selection of friction terms even though we may have no clear knowledge of whether we are using the proper terms, the proper values for these teens, or even the proper model!

Although use of a physical model may be very appealing to some, (terrain, friction, and material properties are plugged in and the computer spits out velocity and runout extend), the assumptions used in the models are largely unsupported at the present time. Therefore, because of the problems discussed above in obtaining ground truth in major avalanches, the physical models should not, in my opinion, be used as the only method to predict avalanche runout distance. However, because the physical models are essential in predicting velocity, they must often be used in practice in spite of their limitations.

COMBINATIONS OF TECHNIQUES TO CALCULATE RUNOUT ANDVELOCITY

As mentioned in the beginning of this article, avalanches, although they are special to us, are also analogous to many other geophysical processes. Floods are a particularly useful analogy and as mentioned, delineation of the "100-year flood has received the attention of many scientists and engineers worldwide for most of this century. Avalanche-engineering specialists should look closely at procedures used in analysis of similar geophysical processes because so little research is being conducted in our field.

Drawing a flood boundary is similar to drawing an avalanche runout-zone boundary and often proceeds as follows:

a. The flood discharge, or volume of water flowing past a point per second, is calculated by studying the flood history of the region, a statistical method.

b. The flood boundaries are calculated by using the discharge (calculated in step "a'"), in a physical model that considers the stream bed roughness, slope, and cross-sectional shape.

Although avalanches only resemble floods superficially, the runout-distance and velocity calculation procedures can be quite similar to those used in flood studies. Are commended 2-step procedure could be as follows.

a. The runout distance is determined from the historical record when the record is long and continuous, by vegetation damage or the geological record when this is unmistakable, and from statistical models derived from the mountain region of interest. The stopping position is not calculated from a physical model.

b. Avalanche velocity is calculated by using a physical model, however that model is forced to stop at the position determined in step "a." The physical model thus calculates design velocities along the path profile.

I think this "2-step approach" to determining the design avalanche characteristic is superior to relying primarily on a physical model alone. The subjectivity is reduced because the runout distance is determined from the statistics of major avalanche in the area. A physical model is used, where design velocity information is required in structural defense or other engineering applications. This 2-step approach is also consistent with analysis of similar geophysical processes.

CONCLUSIONS

Obviously, no "cookbook"solutions to the engineering problems of determining designavalanche runout and velocities have been discussed in this article. The complex interactions of avalanche terrain and material properties should in fact force any analysis to rely on multiple procedures. Even the best and most reliable methods available will produce misleading or unrealistic estimates of velocity and runout in some cases where there are simply no "recipes" available in any cookbook.

The various analytical methods will never be perfect and may never attain the refinement and acceptability of methods used by flood hydrolists regardless of how our "state of the art" progresses. There are simply not enough people doing research and applying current procedures. The best available current methodologies, however, should always be applied, regardless of the imperfections that continue to exist. This trialand-error process is normal in science and engineering. When it is allowed to operate over a period of time, the inevitable mistakes will lead to more accurate, dependable predictions of geophysical processes in general and snow avalanches in particular.

ADDITIONAL READING

This short list of references is by no means comprehensive. It is intended only to give a brief introduction to the subjects of avalanche runout and velocity prediction.